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Connectionist teaching

I recently read the study by Askew et el (1997) called Effective teachers of numeracy in primary schools: teachers beliefs practices and pupils learning and it introduced me to a term called connectionist teaching. Connectionist teachers have "beliefs based around both valuing pupils methods and teaching strategies with an emphasis on establishing connections within mathematics." The study compared this style of teaching with discovery teaching and transmission teaching. It found that teachers with a strong connectionist orientation are more likely to have classes that made greater gains than those classes of teachers with strong discovery or transmission orientations. 

So what do connectionist teachers do?

According to the study, connectionist teachers lessons are generally characterised by a high degree of focused discussion. These discussions were carefully monitored to bring out key strategies and ideas on the concept being taught. Pupils were expected to be able to explain their thinking process rather than just giving an answer to a question. 

Connectionist teachers make "connections within mathematics." For example showing how expanding brackets in algebra has similarities to multiplying integers, rather than trying to link to real life contexts. I believe the most effective way of making those connections is through showing multiple representations. By using a consistent representation for multiple topics, students are able to notice similar methods and strategies. Below are a few examples from twitter of using representations to show a concept. 

Visually solving equations using algebra counters and a vector model. @MEJ0778 
Gattegno charts showing the effect of multiplying by 10, 2 and then linking to indices within algebra. @MrACrampton

Making use of bar modelling on mathsbot.com to find a fraction of an amount. Could also link to sharing in a ratio.
I don't think we should overwhelm students with 5 or 6 representations for the same thing however if we carefully choose them we can use it to enhance understanding and make connections between topics. 

Connectionist teaching is not a complete contrast to discovery or transmission but embodies the best of both of them in its acknowledgment of the role of both the teacher and the pupils in lessons. I like to think of it as being teacher directed as opposed to teacher led or pupil led. 




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